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In order to simulate elastic wave propagation in a complex structure withinhomogeneous media, we often need to obtain the propagating eigenmodes of anelastic waveguide. As the waveguide is assumed uniform in one direction, theoriginal 3-D problem can be converted into a so-called 2.5-D problem by usingthe Fourier transform in that direction. However, the introduction of elasticmetamaterials (EMM) broadens the horizon of this subject, and new features arerequired in EMM waveguides that cannot be obtained by most traditionalwaveguide solvers. In this work, a spectral element method (SEM) is developedto simulate the elastic/acoustic waveguide problem in anisotropic media withanisotropic mass density and/or negative index parameters. To the best of ourknowledge, the SEM has not been introduced previously for such a waveguideproblem. For waveguides with anisotropic density that cannot be solved by theFEM in most of commercial software packages, we design an anisotropic densityEMM waveguide with our SEM solver to demonstrate some intriguing phenomena. Thespectral element results are verified by several numerical examples throughcomparison with the traditional finite element method (FEM) to show itssignificant advantages in term of accuracy and computation efficiency.

Spectral Element Method for the Elastic/Acoustic Waveguide Problem in Anisotropic Metamaterials